Proximal Operator of $ \lambda \left\| W \right\|_1 + \gamma \sum_{i=1}^{k} \left\| G_i \right\|_2 $ ($ {L}_{1} $ Norm and Group Regularization)

Question

Hellow everyone.

I have function $g(W)=\lambda |W|_1 + \gamma \sum_{i=1}^{k} ||G_i||_2$ where $|W| \in R^{m \times T}$ and $G_i \in R^T$, which is preselected rows of $|W|$. I would like to compute the proximal of the $g(W)$ I was wondering whether can someone help me to drive the proximal of $g(W)$